For highly precise production or precision machining of drilled holes, frictional tools are usually used as precision machining tools or what are known as finishing tools. A frictional tool of this type can be gathered, for example, from US 2003/0156912 A1. Frictional tools of this type usually have a plurality of (reaming) cutting edges which are arranged in each case on a common cutting circle, that is to say are at the same radial spacing from a tool center axis. For precision machining of a drilled hole, the frictional tool is guided up to said drilled hole. Firstly the exact roundness of the drilled hole but also the exact orientation along a desired drilled hole longitudinal axis are decisive for highly precise drilled-hole machining. In order to ensure this, the center or rotational axis of the frictional tool has to coincide with the desired setpoint longitudinal axis of the drilled hole and also has to be oriented exactly with respect to said longitudinal axis. In the real world application situation, however, there is the problem that these two preconditions are not always met in a satisfactory manner.